lesson 1.1 expressions and variables september 15, 2008 expressions and variables 1.1 lesson goal:...

Lesson 1.1Expressions and Variables

September 15, 2008

Expressions and Variables1.1 L

ES

SO

N

Goal: Students will be able to evaluate and write variable expressions

Agenda: 1.Check hmwk with partner2.Review 1.13.Begin lesson 1.2

Review: How are numerical and variable expressions similar?

Numerical Variable

Vocabulary• numerical expression

• variable

• variable expression

• evaluate

• verbal model


ES

SO

N


ES

SO

N

Page 8 Number 51 (independent work)

Zach belongs to an online DVD rental

service. His yearly rental budget is

$200 (wow!). Each rental costs $4.00.

1. Copy and complete the table.

DVDs

1

2

3

4

Cost ($)

4

8

?

?

Amount left

196

192

?

?2. Write a variable expression for the cost of r rentals.

3. Write variable expression for the amount of his budget left after r rentals.

DVDs

1

2

3

4

Cost ($)

4

8

12

16

Amount left

196

192

188

184

Writing: How many DVDs will Zach be able to rent before the $200 is spent? Explain how you found your answer.

Sample Answer: Zach could rent 50 DVDs. There is a pattern with the number of DVDs rented and the cost—each number of DVDs rented is multiplied by 4. Therefore, 50 * 4 = 200, which allows Zach to spend the entire $200 without going over his budget.

Remember to show all work when completing problems

Lesson 1.2Powers and Exponents

September 15, 2008

Powers and Exponents1.2 L

ES

SO

N

Goal:

Students will be able to use powers to describe repeated multiplication.

CB Standards We are Working Towards:

2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.8 Use algebraic methods to describe patterns

Assessment: Teacher Observation; Checkpoints


ES

SO

N

Math Message

Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends. How many people have received that email?

What are a few ways you might go about solving this problem.

Table Talk

Vocabulary: Match the vocab wd to the

best definition

1. power

2. base

3. exponent

53

1. It is the result of a repeated multiplication of the same factor

2. Top number of the power

3. Bottom number of the power


ES

SO

N

How to read powers

Power In Words Value

51

55 to the first power

(0.5)2

0.5 to the second power; 0.5 squared

(0.5)(0.5) = 0.25

53

54

5 to the third power; 5 cubed

5 to the fourth power

5*5*5= 125

5*5*5*5= 625


ES

SO

N

Example 1: Write the product using an exponent

a. 2*2*2*2 = 24

b. (0.2)(0.2)(0.2)=______

c. n * n * n * n * n = ______


ES

SO

N

Checkpoint-use dry erase board to solve

Directions: Write the produce using an exponent.

1. (4.3)(4.3) =_____

2. x * x * x * x =_____


ES

SO

N

Example 2: Evaluating Powers with Variables

Evaluate the expression x when x = 0.54

CheckpointEvaluate the expression when x = 3

m

m

2

4

=

=


ES

SO

N

Example 3: Using Powers in FormulasWhat formulas require the use of powers?

Area in square units; Volume in cubic units


ES

SO

N

Example 3: Using Powers in Formulas

Brandon is going to use cube-shaped block of ice to make an ice sculpture for a competition. Find the volume of the ice.

20 in.

20 in.20 in.

V = s 3

Step 1: Write the formula

= (20) Step 2: substitute 20 for s

= (20)(20)(20) Step 3: evaluate the power

3

Answer: The volume of the block of ice is 8,000 cubic inches.

= 8,000 Step 4: multiply

Checkpoint

Find the area of a square with the given side length

• 9 meters

9 meters

A = 81 meters squared


ES

SO

N

Math Message

Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends, and so on.


ES

SO

N

How did you use powers in this problem to describe repeated multiplication?

Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends, and so on.

How would this chart look if we continued the pattern?

Stage Emails Sent as Power Value of Power1 4 4

2 4 16

3 ____ ___

4 ____ ___

1

2

94 262,144 emails9

#s 6, 8, 11

• I will be the reporter

• Need a volunteer to be the recorder at the front board

Math Matters Partner Work

• Page 12 #s 14-28 evens • Label notebook with page # • Read all directions• Show all work• Be neat• When finished you may play 24• We will check as whole group in

approximately 12 minutes

Closing

• Written Response

• Page 13 # 34

• Use complete sentences

• Will review as whole class

Homework

• Page 8 #39 (check in back of book)

• Page 9 #s 57-60 all and #67

• Label each piece of hmwk with page number

• Show all work in notebook

• Be neat

Lesson 1.2Powers and Exponents

September 16, 2008


ES

SO

N

Goal:

Students will be able to use powers to describe repeated multiplication.Check hmwk with partner (star/circle items you’d like to review)• Page 8 #39 (check in back of book)• Page 9 #s 57-60 all and #67




Whole ClassRevisit Lesson 1.2

• Page 12 # 4 and # 12

• I need a recorder, please.

Powers and Exponents

p. 13 #36

• Properly label your notebook

• Be neat

• Show all work

• You may work with a partner

• Play 24 when finished; we will review as whole group in approximately 5 minutes

1.2 Practice A• #s 3, 6, 12, 16, 18, 25, 26• With a partner, create a problem similar to #31

– Be neat and creative– Solve showing all of your work


Play 24 when finished

Will share problems in approximately 18 minutes

• Visit http://fvollman.wikispaces.com

• Helpful websites

• Portaportal for Math

• Textbook

• Section 1.2 online worksheet

• http://snipurl.com/3qlw2

Homework•Practice Wksh 1.2

•3-29 odds only

•Label notebook with Practice wksh 1.2

•Show all work in notebook

•Be neat

•Quiz on lessons 1.1-1.3 on Friday, September 19


Label notebook for hmwk each night; example for tonight your notebook should look like:

Practice Wksh 1.2 #s 3-29 odds 9/16/08

3.

Lesson 1.3September 17, 2008

Order of Operations1.3 L

ES

SO

N

Goal: Students will be able to use order of operations to evaluate numerical and variable expressions.

Check hmwk with partner(star items you’d like to review)• Practice Wksh 1.2• #5-29 odds




How does the order of

operations pertain to this

plant??!!

The Boojum Plant

It is a strange plant that is found in Baja, California. It was founded by Godfrey Sykes in 1922. He named it after a mythical creature in the poem “The Hunting of the Snark”. This creature was found in desolate, far away places. The name suits it quite well!

http://farm3.static.flickr.com/2318/2145881083_d46bb61fd8.jpg?v=0

http://www.bajainsider.com/baja-life/plants-animals-baja/insider_boojum.htm


ES

SO

N

Order of operations:

1. Evaluate expressions inside grouping symbols

2. Evaluate powers

3. Multiply and divide from left to right

4. Add and subtract from left to right

PEMDAS

Please Excuse My Dear Aunt Sally

set of rules for evaluating expressions

involving more than one operation


ES

SO

N

Table Talk: Why might order of operations be important when finding the total number of flowers in the flag?

•About 2,000 plants in each of the 50 stars of this flower flag.

•There about 64,100 plants in each of the 7 short stripes

•106,700 plants in each of the 6 long stripes

•The blue region contains about 198,900 plants


ES

SO

N

There are about 2,000 plants in each of the 50 stars of this flower flag. There about 64,100 plants in each of the 7 short stripes and 106,700 plants in each of the 6 long stripes. The blue region contains about 198,900 plants. Write a numerical expression to find the total number of plants.

50 * 2000 + 7 * 64,100 + 6 * 106,700 + 198,900

100,000 + 448,700 + 640,200 + 198,900

Approximately 1,387,800 were used in this flower flag


ES

SO

N

Order of operations:

1. Evaluate expressions inside grouping symbols

2. Evaluate powers

3. Multiply and divide from left to right

4. Add and subtract from left to right

PEMDAS

Please Excuse My Dear Aunt Sally

set of rules for evaluating expressions

involving more than one operation


ES

SO

N

Using Grouping Symbols

Directions: Evaluate the expression

a) 8(17 – 2.3) =

= 8 (14.7)

= 117.6

Show all of your work

14.7

* 8


ES

SO

N

Using Grouping Symbols


14 + 612-7

= (14 + 16) (12-5) Rewrite the fraction as division

20 5 =

4

Evaluate within parentheses

Divide


ES

SO

N

What other type of grouping symbol might you see this year?


= 5 * [ 36 – ( 22)]

14

36

-22

c) 5 * [ 36 – ( 13 + 9 )] =

= 5 * 1414

• 5

70

70

Work from inner symbol

to the outer symbol


ES

SO

N

Checkpoint

1. 10 ( 1.5 + 0.6)

2. 72 [(11 – 7) * 2]

21

9


ES

SO

N

Page 18 1. Give three examples of grouping symbols.

•Numbers 4, 6, 7, 8

•We will use the board and the overhead.

•All eyes on board; you will be told when to write

Students will be able to use order of operations to evaluate expressions.

Number 28

The Boojum Plant

http://farm3.static.flickr.com/2318/2145881083_d46bb61fd8.jpg?v=0

A boojum is a very slow-growing cactus. One fifty-year-old boojum is 1.5 meters tall, and has been growing about 0.03 meter each year. Assume the same pattern keeps going.

There are 3.28084 feet in a meter.

2. How tall will the boojum be 50 years from now?

1. Write an expression for the height in meters of the boojum y years from now.

Variable Expression:1.5 + 0.03y

1.5 + 0.03y1.5 + 0.03(50)1.5 + 1.5 =3The boojum would grow 3 meters.

Remember your goal: You will be able to use the order of operations to evaluate numerical and variable expressions.

With your Math Matters Partner you will visit

http://fvollman.wikispaces.com

“helpful websites”

Login as a guest—fvollman

Think through activities under Math-Order of Operations


ES

SO

N

Students will be able to use order of operations to evaluate expressions.

The table shows the numbers of sets of twins, triplets, quadruplets, and

quintuplets registered at a twin convention. Write and evaluate an

expression for the total number of people who registered at the convention.

Type Sets

Twins 2697

Triplets 29

Quadruplets 2

Quintuplets 1

Wksh 1.3A#s 12-28 evens onlyShow all work neatly in notebook

Label notebook for hmwk each night; example for tonight your notebook should look like:

1.3 Practice A #s 12-28 even 9/17/08

12.

lesson 1.1 expressions and variables september 15, 2008 expressions and variables 1.1 lesson goal:...

Documents